There is only one thing to consider when loading up on gems, enchants, and glyphs. That is a simple and effective approach that I've followed for many years. How will these enchants help me kill a zombie. That's right. Think about it! Zombies and Ghouls in WoW hold the very core of the different abilities that others use. They can use magic to some extent, spew poison and disease, hit really hard, and can even run pretty fast. If thinking about zombies gives you the shivers then I'll use a secondary approach. Think about Murlocs. No one wants to think about Murlocs, though.
Think about this. Every enemy in the game, and especially zombies, want to run up to you and shred you apart and as a Mage you have the inherent disadvantage of wearing nothing more than paper and pretty dresses. So you need to blast them away before they can get to you (think of your spells as a shotgun). Now a zombie isn't going to easily be taken down with one or two measly blasts, no no no. So you need to enhance that weapon any way you can to get the absolute most out of it so that the hordes of Zombies, Ghouls, and now Geists don't run you over (or to some extent Patchwerk, Kel'Thuzad, and the cute XT-002 Deconstructor). Every point counts. No matter how insignificant you think that point is, every single drop of extra power counts.
Enchants come from Enchanters who are other player characters that took up the Enchanting profession. It'll often require you buying the ingredients to brew up the enchant and then talk with another player who will use their profession on your gear. One key tip is to always put the item you wanted enchanted in the "Do Not Trade" tab. Your guild might have an Enchanter and most major cities General/Trade chats have tons of them. So don't worry about finding one.
Enchants can be applied to various pieces of clothing and then some enchants in the form of items can be applied to others. Head, shoulder, and legs are done through Arcanums, Inscriptions, and Leg Armor respectively. The Waist slot can take a Belt Buckle that'll give it another gem slot but doesn't have any specific enchants. The rest are done by Enchanters.
What are you looking for? Well the simple answer is spell power. Enchanting for spell power is never the wrong choice and many high end enchants come free with bonus critical strike rating so you get the best of both worlds. However, getting the best enchants for low end gear or gear that you will soon replace is always a bad idea. You don't want to go broke constantly enchanting gear with the best when you'll get something to replace it next week. That's why you should sit down and get out a sheet of paper and write down what you want on a budget and what you want on the high end. Below are some examples, but sometimes you may be using a non-standard build or a build that requires a certain stat here or there so be sure to look over what you can get before you commit.
Head: Arcanum of Burning Mysteries is 150gold and somewhat expensive so going without a head enchant is perfectly fine, but if you have Revered with either the Sha'tar you can pick up 22 spell power and 14 hit rating for 100 gold (50 gold cheaper). When you're not needing the best, the extra hit rating will help and they're easy to replace. Otherwise, don't worry about a head slot enchant.
Shoulders: For the cheap one, you're going to want to go back to Outland and pick up exalted with the Scryers or the Aldor. Get one of their inscriptions and use it. At higher levels you can farm up tons of Librams so don't sweat the cost so much.
Cloak/Back: Well, for the money you might want to get Speed (15 haste rating) on your cloak or maybe Spell Penetration (20 spell penetration). Those are the cheapest enchants you can pick up.
Chest: Super Stats (+8 all stats) is the no brainer.
Wrist: Greater Spell Power (23 spell power) is perfectly fine.
Hands: Major Spell Power (20 spell power) is a good choice or Precise Strikes (15 hit rating) is another good one if you're low on hit.
Legs: Pick up some Azure Spellthread (35 spell power, 20 stamina) on the cheap or just skip this slot on a budget. If your guild is into running older instances you can skip back to Zul'Gurub and get the leg enchants there, but it's not the best idea to go out of your way for it.
Feet: Speed is the name of the game for your feet so snag Boar's Speed (8% run speed, 15 stamina).
Weapon (1-hand): Major or Exceptional Spellpower (40/50 spell power)
Weapon (Staff): Enchant Staff Spell Power (69 Spell Power)
Full Out Enchants
Are you a tailor? Well, you're going to want Lightweave and you need to be a tailor for it!
Head: Arcanum of Burning Mysteries (Revered with Kirin'Tor)
Shoulders: Greater Inscription of the Storm (24 spell power/15 critical strike rating) (Sons of Hodir Exalted)
Back: Lightweave Embrodiary (Tailor Only) or Greater Speed (23 haste rating)
Chest: Powerful Stats (+10 all stats)
Wrist: Superior Spellpower (30 spell power)
Hands: Exceptional Spellpower (28 spell power)
Legs: Sapphire Spellthread (50 spell power/30 stamina)
Feet: Tuskarr's Vitality (15 stamina/8% run speed) or Icewalker (12 hit rating/12 critical strike rating)
Weapon (1-hand): Mighty Spellpower (63 spell power)
Weapon (Staff): Enchant Staff - Greater Spellpower (81 spell power)
Gems are very complex and very difficult to tell you what's best and what's not because everyone has a different taste and there are so many gems out there that you have so many choices on what you want to do and where you want to go. Some people like to stack critical strike rating and rely on the massive blasts while some like to stack spell power for the overall constant flow of damage and SOME like to stack up on hit rating to get over their lack in gear. It's all about what you want and where you want it.
Let's use the Zombie analogy again. Zombies do not care about gems because they only want your brains which are covered in a pita bread like covering. You can reinforce your pita bread with a meta gem that might give that Zombie indigestion as he eats on you or you can use the gems powers to boost your abilities enough to get those few extra points of damage to blast him away before he can get his mouth around you. Remember that every single little bit helps. You never know when those 2 or 3 points of damage will win the battle.
As for the best gems? Well again that's subjective but there are a few good tips to point out. Spell power is a safe bet in PvE and haste rating is always a good secondary stat and so is critical strike. Always get the socket bonuses too, unless the gems you put in will outdo whatever you gain from the socket bonus.
Good gems to snag? Well for a meta socket I'd recommend Chaotic Skyflare Diamond which gives 21 critical strike rating and 3% critical strike damage. Doesn't have all the nifty bells and whistles other gems have but does give you an exceptional boost in damage. Rune Scarlet Rubies (19 spell power), Reckless Monarch Topaz (9 spell power and 8 haste rating), and Glowing Twilight Opals (9 spell power and 12 stamina) are some of the better picks. Anything with spell power or critical strike is good to use for the Mage.
Other Tips & Pointers
Overall just aim to work on a budget build as you start getting gear. Work on the target dummies and see where you gain the most DPS. Use addons like Recount to see how much damage you do with your spell rotation when you're wearing certain gems and try to min/max as much as you can. By the time you get your high end set you'll have a really good feeling about what enchants and gems you'll want and Zombies will no longer be a worry for you (but 50 foot tall robots may still be).
If you need some help, remember that spell power and critical strike are always safe bets and the more the better. Don't spend 1,000 gold on greens and blues and don't spend 100 gold doing a full set of the highest tier gear. Be realistic about your wants and you'll be a pro player in no time.